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One-Sided Limits - Worksheet 5 - 12th Grade

Medium

Evaluate limits with the approach direction stated and distinguish limits from function values.

medium: Practice the same exercise types with a fresh numbered set.

22 problems · 20-25 minutes · Skills: limits, calculus, continuity

About This Worksheet

This medium-level worksheet contains 22 problems designed for 12th Grade students practicing one-sided limits. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Manipulate algebraic expressions and understand functions, limits and derivative notation.

  • Evaluate limits with the approach direction stated and distinguish limits from function values.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: f(x) = 7 when x < 4, and f(x) = 11 when x ≥ 4. Find the limit as x approaches 4 from the left.
Solution Steps:
  1. Use the branch on the requested side of the boundary.
  2. A one-sided limit need not equal the limit from the other side.
Answer: 7
Tip: Check your result using the method in the example before moving to the next question.
1
f(x) = 7 when x < 2, and f(x) = 10 when x ≥ 2. Find the limit as x approaches 2 from the left.
2
f(x) = 7 when x < 7, and f(x) = 11 when x ≥ 7. Find the limit as x approaches 7 from the right.
3
f(x) = 2 when x < 4, and f(x) = 4 when x ≥ 4. Find the limit as x approaches 4 from the left.
4
f(x) = 1 when x < 7, and f(x) = 4 when x ≥ 7. Find the limit as x approaches 7 from the right.
5
f(x) = 6 when x < 4, and f(x) = 9 when x ≥ 4. Find the limit as x approaches 4 from the left.
6
f(x) = 5 when x < 7, and f(x) = 10 when x ≥ 7. Find the limit as x approaches 7 from the right.
7
f(x) = 1 when x < 8, and f(x) = 10 when x ≥ 8. Find the limit as x approaches 8 from the left.
8
f(x) = 7 when x < 3, and f(x) = 13 when x ≥ 3. Find the limit as x approaches 3 from the right.
9
f(x) = 5 when x < 5, and f(x) = 14 when x ≥ 5. Find the limit as x approaches 5 from the left.
10
f(x) = 5 when x < 4, and f(x) = 8 when x ≥ 4. Find the limit as x approaches 4 from the right.
11
f(x) = 8 when x < 3, and f(x) = 11 when x ≥ 3. Find the limit as x approaches 3 from the left.
12
f(x) = 9 when x < 4, and f(x) = 12 when x ≥ 4. Find the limit as x approaches 4 from the right.
13
f(x) = 3 when x < 8, and f(x) = 8 when x ≥ 8. Find the limit as x approaches 8 from the left.
14
f(x) = 8 when x < 3, and f(x) = 14 when x ≥ 3. Find the limit as x approaches 3 from the right.
15
f(x) = 6 when x < 4, and f(x) = 8 when x ≥ 4. Find the limit as x approaches 4 from the left.
16
f(x) = 1 when x < 2, and f(x) = 4 when x ≥ 2. Find the limit as x approaches 2 from the right.
17
f(x) = 3 when x < 7, and f(x) = 5 when x ≥ 7. Find the limit as x approaches 7 from the left.
18
f(x) = 2 when x < 4, and f(x) = 6 when x ≥ 4. Find the limit as x approaches 4 from the right.
19
f(x) = 7 when x < 1, and f(x) = 10 when x ≥ 1. Find the limit as x approaches 1 from the left.
20
f(x) = 6 when x < 3, and f(x) = 13 when x ≥ 3. Find the limit as x approaches 3 from the right.
21
f(x) = 1 when x < 2, and f(x) = 7 when x ≥ 2. Find the limit as x approaches 2 from the left.
22
f(x) = 9 when x < 8, and f(x) = 11 when x ≥ 8. Find the limit as x approaches 8 from the right.

Answer Key

1. 72. 113. 24. 45. 66. 107. 18. 139. 510. 811. 812. 1213. 314. 1415. 616. 417. 318. 619. 720. 1321. 122. 11

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Frequently Asked Questions

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What skills does this limits & continuity worksheet cover?

This worksheet focuses on limits, calculus, continuity. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 22 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.